; 


DANlEPCfUNDERHIL! 


University  of  California  •  Berkeley 


THE  THEODORE  P.  HILL  COLLECTION 

of 

EARLY  AMERICAN  MATHEMATICS  BOOKS 


THE   ARITHMETICAL   PRIMER. 

OTIDISIEMItWS 

NEW  TABLE-BOOK; 


OR, 


TABLES  OF  ARITHMETIC  MADE  EASIER, 

BY  D.  C.  UNDERBILL, 

FORMERLY  TEACHER  IN  FRIENDS*  SCHOOL,  NEW  YORK. 


A    NEW    EDITION, 
KEVISED,  ENLARGED,  AND  IMPROVED. 


NEW  YORK: 
M.  F.  C.  MARSH,    55    FULTON     STREET. 


I 


PREFACE. 


UNDERBILL'S  NEW  TABLE-BOOK,  which,  under  one  name  or  another, 
has  for  so  many  years  enjoyed  popular  favor,  is  now  presented  to  the 
public  in  an  enlarged  and  improved  form,  and  in  a  more  worthy  style  of 
typography. 

Alphabetical  primers  are  no  novelty ;  the  present  book,  in  its  various 
editions,  has  been  as  yet  the  first  and  only  attempt  to  produce  an  arith- 
metical primer  fitted  to  initiate  the  young  into  the  mysteries  of  figures, 
and  to  render  the  subject  of  numbers,  in  their  uses  and  applications, 
attractive  rather  than  repulsive  to  children. 

A  number  of  new  pictorial  illustrations  will  be  found  in  the  present 
edition.  The  Tables  of  Money,  Weight,  Measure,  &c.,  hare  also  been 
inserted  in  verse  as  well  as  in  the  standard  form,  in  order  to  fix  the  facts 
permanently  in  the  mind  of  the  learner,  so  that  they,  either  from  memory 
or  association,  may  be  as  promptly  reproduced,  when  needed,  as  that 
universal  one  which  recalls  the  number  of  days  in  each  month. 

It  is  only  necessary  to  add  that  this  little  book  is  suited  to  the  capacity 
of  every  child  who  is  able  to  read,  that  it  is  designed  to  meet  the  wants 
of  schools  in  every  section  of  tfte  country,  and  is  equally  well-adapted 
for  home  or  parental  instruction. 


Entered,  according  to  Act  of  Congress,  in  the  year  1846,  by  FKIOK  ADAXS.  and  re 

entered  in  the  year  1854,  by  WM.  P.  COOLSDGK,  in  the  Clerk's  Office  of  the 

Drstrict  Court  for  the  Southern  District  of  New  York 


Notation.~Tal>Ie  of  Figures. 

ARABIC. 

1234567§910 

ROMAN. 

I      II. -III.    IV     V     VI.     VII      VIII     IX.     X. 

WRITTEN. 

4234-5673940 


MwMV0b?«0W«S»«0«S9Ca?«SS«8»«S0*P*SSM0BaVW«a0WVWW«*WW0W«aP«0a0«0«WtMB9M«M 

NUMERATION 

OF 

Roman  and  Arabic  Figures. 

4     Roman.                          Arabic. 

Roman.                          Arabic. 

I    One                              1 

XXX.  Thirty      ...  30 

II.  Two     ....     '2 

XXXI.  Thirty-one  -     -     31 

4          III.  Three    ....     3 

XL.  Forty  ....  40 

IV.  Four    ....       4 

XLI.   Forty-one    -     -     41 

V.  Five      ....     5 

L.  Fifty   ....  50 

VI.  Six      ....       6 

LI.   Fifty-one     -     -     51 

VII.  Seven    ....     7 

LX.  Sixty  ....  60 

VIII.  Eight  ....       8 

LXI.  Sixty-one    -     -     61 

IX.  Nine      -     -     -     -     9 

LXX.  Seventy   -     -     -  70 

X.  Ten      -     ---     10 

LXXI.  Seventy-one     -     71 

XI.  Eleven  -     ...  11 

LXXX.  Eighty     ...  80 

1         XII.  Twelve     -     -     -     12 

LXXXI.  Eighty-one       -     81 

XIII.  Thirteen    "...  13 

XC.  Ninety     -     -     -  90 

!XIV.  Fourteen-     -     -     14 

XCI.  Ninety-one       -     91 

XV.  Fifteen  ....  15 

XCV.  Ninety-five    -     -  95 

XVI.  Sixteen     -     -     -     16 

XCIX.  Ninety-nine     -     99 

XVII.  Seventeen  -     -     -  17 

C.   1  hundred  -     -  100 

XVIII.  Eighteen-     -     -     18 

CO.  2  hundred      -     200 

XIX.  Nineteen    ...  19 

CCC.  3  hundred  -     -  300 

XX.  Twenty    -     -     -     20 

CCCC.  4  hundred      -     400 

XXI.  Twenty-one     -     -  21 

D.  5  hundred  -     -  500 

XXII.  Twenty-two  -     -     22 

DC.  6  hundred      -     600 

XXIII.  Twentv-three  -     -  23 

DOC.  7  hundred  -     -  700 

XXIV.   Twenty-four-     -     24 

DCCC.  8  hundred      -     800 

XXV.  Twenty-five     -     -  25 

DCCCC.  9  hundred  -     -  900 

XXVI.  Twenty-six    -     -     26 

M.   1  thousand     -  1000 

w      XXVII.  Twenty-seven    -  27 

M.DCCC.LIV.    One  thousand 

4    XXVIII.  Twenty-eight.    -     28  j                         eight  hundred  and 

|       XXIX.  Twenty-nine-     -  29  (                         fifty-four,  1854. 

NOTE.  —  The  Roman  characters  are  seven  in  number  —  I  V.  X.  L.  C.  D. 

^    M.  —  and  any  number  may  be  formed  by  combinations  of  them. 
31         The  repetition  of  a  letter  repeats  its  value  in  the  number.     X  being 
3,    ten,  XX  make  twenty,  XXX  thirty,  &c.    A  letter  of  less  value,  placed 

^     at  the  right-hand  of  one  of  a  greater  value,  increases  the  number  ;  placed 
^     at  the  left-hand,  it  diminishes  the  number.     Thus,  V  being  five,  and  I  one, 

!     VI  is  six,  and  IV  four  ;  XI  eleven,  and  IX  nine,  &c, 

j,        The  Roman  mode  of  numbering  is  now  but  little  used;  the  Arabic 

1    being  preferred  for  business  and  other  purposes. 

Numeration. 

123456789  10 


How  many  balls  are  there 
in  each  line,  counting  three 
ways  ?  Begin  at  1,  and 
count  all  around  on  the  out 
side  back  to  1  again,  and 
see  if  there  are  not  twenty- 
seven.  Then  count  the 
whole,  and  see  if  there  are 
not  55 


Read  the  following  numbers : — 


45,  78,  67,  13,  46,  79,  35,  68. 
70,  49,  82,  43,  76,  17,  50,  83. 
85,  20,  53,  41,  74,  87,  42,  75. 
11,  44,  25,  91,  77,  26,  59,  33. 


14,  80,  36,  69,  15,  48,  81,  37. 
38,  18,  51,  84,  39,  72,  19,  52. 
22,  55,  88,  23,  56,  24,  57,  90. 
92,  66,  27,  60,  93,  32,  65,  94. 


NUMERATION   TABLE. 

The  amount  expressed  by  figures  increases  from  right  to  left, 
but  in  reading  or  numerating  them,  commence  at  the  left  hand. 


5 


Table  of  Addition. 


1 

and 

1 

are 

2 

2 

and 

1 

are 

3 

1 

and 

2 

are 

3 

2 

and 

2 

are 

4 

1 

and 

3 

are 

4 

2 

and 

3 

are 

5 

1 

and 

4 

are 

5 

2 

and 

4 

are 

6 

1 

and 

5 

are 

6 

2 

and 

5 

are 

7 

1 

and 

6 

are 

7 

2 

and 

6 

are 

8 

1 

and 

7 

are 

8 

2 

and 

7 

are 

9 

1 

and 

8 

are 

9 

2 

and 

8 

are 

10 

1 

and 

9 

are 

10 

2 

and 

9 

are 

11 

1 

and 

10 

are 

11 

2 

and 

10 

are 

12 

1 

and 

11 

are 

12 

2 

and 

11 

are 

13 

1 

and 

12 

are 

13 

2 

arid 

12 

are 

14 

3 

and 

1 

are 

4 

4 

and 

1 

are 

5 

3 

and 

2 

are 

5 

4 

and 

2 

are 

6 

3 

and 

3 

are 

6 

4 

and 

3 

are 

7 

3 

and 

4 

are 

7 

4 

and 

4 

are 

8 

3 

and 

5 

are 

8 

4 

and 

5 

are 

9 

3 

and 

6 

are 

9 

4 

and 

6 

are 

10 

3 

and 

7 

are 

10 

4 

and 

7 

are 

11 

3 

and 

8 

are 

11 

4 

and 

8 

are 

12 

3 

and 

9 

are 

12 

4 

and 

9 

are 

13 

3 

and 

10 

are 

13 

4 

and 

10 

are 

14 

3 

and 

11 

are 

14 

4 

and 

11 

are 

15 

3 

and 

12 

are 

15 

4 

and 

12 

are 

16 

5 

and 

1 

are 

6 

6 

and 

1 

are 

7 

5 

and 

2 

are 

7 

6 

and 

2 

are 

8 

5 

and 

3 

are 

8 

6 

and 

3 

are 

9 

5 

and 

4 

are 

9 

6 

and 

4 

are 

10 

5 

and 

5 

are 

10 

6 

and 

5 

are 

11 

5 

and 

6 

are 

11 

6 

and 

(> 

are 

12 

5 

and 

7 

are 

12 

6 

and 

7 

are 

13 

5 

and 

8 

are 

13 

6 

and 

8 

are 

14 

5 

and 

9 

are 

14 

6 

and 

9 

are 

15 

5 

and 

10 

are 

15 

6 

and 

10 

are 

16 

5 

and 

11 

are 

16 

6 

and 

11 

are 

17 

5 

and 

12 

are 

17 

6 

and 

12 

are 

18 

TafoSe 

of 

Addition 

.  —  CONTINUED. 

7 

and 

1 

are 

8 

8 

and 

1 

are 

9 

7 

and 

2 

are 

9 

8 

and 

2 

are 

10 

, 

7 

and 

3 

are 

10 

8 

and 

3 

are 

11 

j 

7 

and 

4 

are 

11 

8 

and 

4 

are 

12 

s 

7 

and 

5 

are 

12 

8 

and 

5 

are 

13 

~ 

7 

and 

6 

are 

13 

8 

and 

6 

are 

14 

\t 

1  -, 

7 

and 

7 

are 

14 

8 

and 

7 

are 

15 

7 

and 

8 

are 

15 

8 

and 

8 

are 

16 

!F": 

7 

and 

9 

are 

16 

8 

and 

9 

are 

17 

r 

7 

and 

10 

are 

17 

8 

and 

10 

are 

18 

r 

7 

and 

11 

are 

18 

8 

and 

11 

are 

19 

i 

7 

and 

12 

are 

19 

8 

and 

12 

are 

20 

1 

9 

and 

1 

are 

10 

10 

and 

1 

are 

11 

0 

9 

and 

2 

are 

11 

10 

and 

2 

are 

12 

E 

9 

arid 

3 

are 

12 

10 

and 

3 

are 

13 

y 

9 

and 

4 

are 

13 

10 

and 

4 

are 

14 

|  j 

9 

and 

5 

are 

14 

10 

and 

5 

are 

15 

9 

and 

6 

are 

15 

10 

and 

6 

are 

16 

in 

9 

and 

7 

are 

16 

10 

and 

7 

are 

17 

ip 

9 

and 

8 

are 

17 

10 

and 

8 

are 

18 

i 

9 

and 

9 

are 

18 

10 

and 

9 

are 

19 

9 

and 

10 

are 

19 

10 

and 

10 

are 

20 

s 

9 

and 

11 

are 

20 

10 

and 

11 

are 

21 

!  y 

9 

and 

12 

are 

21 

10 

and 

12 

are 

22 

11 

and 

1 

are 

12 

12 

and 

1 

are 

13 

11 

and 

2 

are 

13 

12 

and 

2 

are 

14 

11 

and 

3 

are 

14 

12 

and 

3 

are 

15 

8 

11 

and 

4 

are 

15 

12 

and 

4 

are 

16 

11 

and 

5 

are 

16 

12 

and 

5 

are 

17 

I 

11 

and 

6 

are 

17 

12 

and 

6 

are 

18 

I 

11 

and 

7 

are 

18 

12 

and 

7 

are 

19 

i 

11 

and 

8 

are 

19 

12 

and 

8 

are 

20 

• 

11 

and 

9 

are 

20 

12 

and 

9 

are 

21 

! 

11 

and 

10 

are 

21 

12 

and 

10 

are 

22  v 

! 

11 

and 

11 

are 

^2 

12 

and 

11 

are 

23 

1  1 

11 

and 

12 

are 

23 

12 

and 

12 

are 

24 

'  g 

Addition  in  Rhyme 


Two  apples  had  Jane, 

And  Mary  2  more, 

They  gave  them  to  Sarah, 

And  then  she  had  4  ; 

Thus,  2  and  2  are  4,  we  know, 

The  apples  make  it  plainly  so. 


James  has  2  pears  we  see, 
Then  suppose  I  give  him  3, 
How  many  will  there  be  ? 
2  and  3  are  5  we  know, 
So  3  and  2  for  5  must  go, 
Look  in  the  table  and  find  it  so. 


Margaret  had  a  pincushion, 
Presented  by  her  mother, 
It  had  5  pins  upon  one  side, 
And  4  pins  on  the  other—- 
On the  little  velvet  ball, 
How  many  pins  were  there  in  all? 
5  and  4,  as  9  we  view, 

And  4  and  5  are  9,  as  true, 

The  table  will  say  the  same  to  you. 


Subtraction  Table. 


1  from  1  leaves  0 
1  from  2  leaves  1 
1  from  3  leaves  2 
1  from  4  leaves  3 
1  from  5  leaves  4 
1  from  6  leaves  5 
1  from  7  leaves  6 
1  from  8  leaves  7 
1  from  9  leaves  8 
1  from  10  leaves  9 
1  from  11  leaves  10 
1  from  12  leaves  11 

4  from  4  leaves  0 
4  from  5  leaves  1 
4  from  6  Leaves  2 
4  from  7  leaves  3 
4  from  8  leaves  4 
4  from  9  leaves  5 
4  from  10  leaves  6 
4  from  11  leaves  7 
4  from  12  leaves  8 
4  from  13  leaves  9 
4  from  14  leaves  10 
4  from  15  leaves  11 

2  from  2  leaves  0 
2  from  3  leaves  1 
2  from  4  leaves  2 
2  from  5  leaves  3 
2  from  6  leaves  4 
2  from  7  leaves  5 
2  from  8  leaves  6 
2  from  9  leaves  7 
2  from  10  leaves  8 
2  from  1  1  leaves  9 
2  from  12  leaves  10 
2  from  13  leaves  11 

5  from  5  leaves  0 
5  from  6  leaves  1 
5  from  7  leaves  2 
5  from  8  leaves  3 
5  from  9  leaves  4 
5  from  10  leaves  5 
5  from  11  leaves  6 
5  from  12  leaves  7 
5  from  13  leaves  8 
5  from  14  leaves  9 
5  from  15  leaves  10 
5  from  16  leaves  11 

3  from  3  leaves  0 
3  from  4  leaves  1 
3  from  5  leaves  2 
3  from  6  leaves  3 
3  from  7  leaves  4 
3  from  8  leaves  5 
3  from  9  leaves  6 
3  from  10  leaves  7 
3  from  11  leaves  8 
3  from  12  leaves  9 
3  from  13  leaves  10 
3  from  14  leaves  11 

0  from  6  leaves  0 
6  from  7  leaves  1 
6  from  8  leaves  2 
6  from  9  leaves  3 
6  from  10  leaves  4 
6  from  11  leaves  5 
6  from  12  leaves  6 
6  from  13  leaves  7 
6  from  14  leaves  8 
6  from  15  leaves  9 
6  from  16  leaves  10 
6  from  17  leaves  11 

9 


Subtraction  Table.— CONTINUED. 


1 


7  from  7  leaves  0 
7  from  8  leaves  1 
7  from  9  leaves  2 
7  from  10  leaves  3 
7  from  11  leaves  4 
7  from  12  leaves  5 
7  from  13  leaves  6 
7  from  14  leaves  7 
7  from  15  leaves  8 
7  from  16  leaves  9 
7  from  17  leaves  10 
7  from  18  leaves  11 

10  from  10  leaves  0 
10  from  11  leaves  1 
10  from  12  leaves  2 
10  from  13  leaves  3 
10  from  14  leaves  4 
10  from  15  leaves  5 
10  from  16  leaves  6 
10  from  17  leaves  7 
10  from  18  leaves  8 
10  from  19  leaves  9 
10  from  20  leaves  10 
10  from  21  leaves  11 

8  from  8  leaves  0 
8  from  9  leaves  1 
8  from  10  leaves  2 
JB  from  11  leaves  3 
8  from  12  leaves  4 
8  from  13  leaves  5 
8  from  14  leaves  0 
8  from  15  leaves  7 
8  from  16  leaves  8 
8  from  17  leaves  9 
8  from  18  leaves  10 
8  from  19  leaves  11 

11  from  11  leaves  0 
11  from  12  leaves  1 
11  from  13  leaves  2 
11  from.  14  leaves  3 
11  from  15  leaves  4 
11  from  16  leaves  5 
11  from  17  leaves  6 
11  from  18  leaves  7 
11  from  19  leaves  8 
11  from  20  leaves  9 
11  from  21  leaves  10 
11  from  22  leaves  11 

9  .from  9  leaves  0 
9  from  10  leaves  1 
9  from  11  leaves  2 
9  from  12  leaves  3 
9  from  13  leaves  4 
9  from  14  leaves  5 
9  from  15  leaves  6 
9  from  16  leaves  7 
9  from  17  leaves  8 
9  from  18  leaves  9 
9  from  19  leaves  10 
9  from  20  leaves  11 

12  from  12  leaves  0 
12  from  13  leaves  1 
12  from  14  leaves  2 
12  from  15  leaves  3 
12  from  16  leaves  4 
12  from  17  leaves  5 
12  from  18  leaves  6 
12  from  19  leaves  7 
12  from  20  leaves  8 
12  from  21  leaves  9 
12  from  22  leaves  10 
12  from  23  leaves  11 

10 


story 


Subtraction  in  Rhyme. 


Three  apples  on  a  table  lie, 

And  Jane  takes  one  in  passing  by; 

How  many  does  she  leave  ? 
1  from  3  leaves  2, 
So  says  the  table  true ; 
And  2  from  3  leaves  1, 
When  the  work  is  rightly  done  ; 
And  so  must  all  believe. 


Charlotte  had  11  pins, 

And  gave  Eliza  4 ; 
Then  all  she  had  remaining 
Were  7  and  no  more. 
4  and  7  make  11, 
Then  4  from  11  leaves  7, 
And  7  from  11,  four. 


Peter  has  just  18  plums, 
And  gives  his  sister  10, 

As  gaily  in  the  room  he  comes  ; 
How  many  has  he  then  ? 

The    table    makes    it    clear    and 
straight, 

That  10  from  18  leaves  just  8', 
And  8  from  18,  ten — 

From  18  plums  take  10  away, 

8  plums  are  left,  'tis  plain  as  day. 


11 


TaMe  of  Multiplication. 


2 

times 

1 

are 

2 

5 

times 

1 

are 

5 

2 

times 

2 

are 

4 

5 

times 

2 

are 

10 

2 

times 

3 

are 

6 

5 

times 

3 

are 

15 

2 

times 

4 

are 

8 

5 

times 

4 

are 

20 

2 

times 

5 

are 

10 

5 

times 

5 

are 

25 

2 

times 

6 

are 

12 

5 

times 

6 

are 

30 

2 

times 

7 

are 

14 

f> 

times 

7 

are 

35 

2 

times 

8 

are 

16 

5 

times 

8 

are 

40 

2 

times 

9 

are 

18 

5 

times 

9 

are 

45 

2 

times 

10 

are 

20 

5 

times 

]0 

are 

50 

2 

times 

11 

are 

22 

,  5 

times 

11 

are 

55 

2 

times 

12 

are 

24 

5 

times 

12 

are 

60 

3 

times 

1 

are 

3 

6 

times 

1 

are 

6 

3 

times 

2 

are 

6 

6 

times 

2 

are 

12 

3 

times 

3 

are 

9 

6 

times 

3 

are 

18 

3 

times 

4 

are 

12 

6 

times 

4 

are 

24 

3 

times 

5 

are 

15 

6 

times 

5 

are 

30 

3 

times 

6 

are 

18 

6 

times 

6 

are 

36 

3 

times 

7 

are 

21 

6 

times 

7 

are 

42 

3 

times 

8 

are 

24 

6 

times 

8 

are 

48 

3 

times 

9 

are 

27 

6 

times 

9 

are 

54 

3 

times 

10 

are 

30 

6 

times 

10 

are 

60 

3 

times 

11 

are 

33 

6 

times 

11 

are 

66 

3 

times 

12 

are 

38 

6 

times 

12 

are 

72 

4 

times 

1 

are 

4          7 

times 

1 

are 

7 

4 

times 

2 

are 

8 

7 

times 

2 

are 

14 

4 

times 

3 

are 

12 

7 

times 

3 

are 

21 

4 

times 

4 

are 

16 

7 

times 

4 

are 

28 

4 

times 

5 

are 

20 

7 

times 

5 

are 

35 

4 

times 

6 

are 

24 

7 

times 

6 

are^ 

42 

4 

times 

7 

are 

28 

7 

times 

7 

are 

49 

4 

times 

8 

are 

32 

7 

times 

8 

are 

56 

4 

times 

9 

are 

36 

7 

times 

9 

are 

63 

4 

times 

10 

are 

40 

7 

times 

10 

are 

70 

4 

times 

11 

are 

44 

7 

times 

11 

are 

77 

4 

=s?^== 

times 

12 

are 

48 

7 

times 

12 

are 

84 

12 


TaR>Ie  of  Multiplication.— CONTINUED. 


8  times     1  are       8 
8  times     2  are     16 
8  times     3  are     24 
8  times     4  are     32 
8  times     5  are     40 
8  times     6  are    48 
8  times     7  are     56 
8  times     8  are     64 
8  times     9  are     72 
8  times  10  are     80 
8  times  11  are     88 
8  times  12  are     96 

1  1  times     1  are     1  1 
11  times     2  are     22 
11  times     3.  are     33 
11  times     4  are     44 
11  times     5  are     55 
11  times     6  are     66 
11  times     7  are     77 
11  times     8  are     88 
11  times     9  are     99 
11  times  10  are  110 
11  times  11  are  121 
1]   times  12  are  132 

9  times     1  are       9 
9  times     2  are     18 
9  times     3  are    27 
9  times     4  are     36 
9  times     5  are     45 
9  times     6  are     54 
9  times     "7  are     63 
9  times     8  are     72 
9  times     9  are  .  81 
9  times  10  are     90 
9  times  11  are     99 
9  times  12  are  108 

12  times     1  are     12 
12  times     2  are    24 
12  times     3  are     36 
12  times     4  are     48 
12  times     5  are     60 
12  times     6  are     72 
12  times     7  are     84 
12  times     8  are     96 
12  times     9  are  108 
12  times  10  are  120 
12  times  11  are  132 
12  times  12  are  144 

10  times     1  are     10 
10  times     2  are     20 
10  times     3  are     30 
10  times     4  are     40 
10  times     5  are     50 
10  times     6  are     60 
10  times     7  are     70 
10  times     8  are     80 
10  times     9  are     90 
10  times  10  are  100 
10  times  11  are  110 
10  times  12  are  120 

13  times     1  are     13 
13  times     2  are     26 
13  times     3  are     39 
13  times     4  are     52 
13  times     5  are     65 
13  times     6  are     78 
13  times     7  are     91 
13  times     8  are  104 
13  times     9  are  117 
13  times  10  are  130 
13  times  11  are  143 
13  times  12  are  156 

Samuel  has  2  knives, 

And  Moses  twice  the  same ; 
How  many  then  for  Moses, 

Ought  we  to  name  ? 
Tic  ice  means  as  many  more, 
Then  Moses  must  have  4  ; 

Twice  1*  are  2, 

Says  the  table  to  you : 

And  twice  2  are  4, 

It  says  furthermore. 


Amelia  has  2  roses, 

And  Frances  has  2  more, 
Miss  Helen  has  another  2, 

To  add  unto  the  4 — 
And  4  and  2  are  6  we  call, 
The  number  which  they  had  in  all : 
So  3  times  2  are  6  we  see, 
And  6  we  say  for  2  times  3. 


Multiplication  in  ISEsyme. 


Four  boys  at  marbles  play, 
And  each  has  5  they  say ; 
How  many  marbles  have  they  all? 
Can  any  one  the  number  call  ? 
Yes,  5  and  5  we  know  are  10, 
Two  other  fives  the  same  again ; 

And  then  2  tens  arc  20  ; 
So  4  times  5  do  20  make, 
And  5  times  4  do  20  take, 
And  here  are  marbles  plenty. 


Division  in  Rhyme. 


Since  2  ones  make  2  we  know, 
Then  2  but  once  in  2  will  go  ; 
Thus  the  father  doth  divide 
2  apples,  one  to  either  side, 
Which  2  good  children  shara 
As  you  can  see  them  there. 


Division  Tatole. 


1  iii     2  goes     2  times 
1  in     3  goes     3  times 
1  in    4  goes     4  times 
1  in     5  goes     5  times 
J.  in     6  goes     6  times 
1  in     7  goes     7  times 
1  in     8  goes     8  times 
1  in     9  goes     9  times 
1  in  10  goes  10  times 
1  in  11  goes  11  times 
1  in  12  goes  12  times 
1  in  13  goes  13  times 

4  in  8  goes  2  times 
4  in  12  goes  3  times 
4  in  16  goes*  4  times 
4  in  20  goes  5  times 
4  in  24  goes  6  times 
4  in  28  goes  7  times 
4  in  32  goes  8  times 
4  in  36  goes  9  times 
4  in  40  goes  10  times 
4  in  44  goes  11  times 
4  in  48  goes  12  times 
4  in  52  goes  13  times 

2  in     4  goes     2  times 
2  in     6  goes     3  times 
2  in     8  goes     4  times 
2  in  10  goes     5  times 
2  in  12  goes     6  times 
2  in  14  goes     7  times 
2  in  16  goes     8  times 
2  in  18  goes     9  times 
2  in  20  goes  10  times 
2  in  22  goes  1  1  times 
2  in  24  goes  12  times 
2  in  26  goes  13  times 

5  in  10  goes  2  times 
5  in  15  goes  3  times 
5  in  20  goes  4  times 
5  in  25  goes  5  times 
5  in  30  goes  6  times 
5  in  35  goes  7  times 
5  in  40  goes  8  times 
5  in  45  goes  9  times 
5  in  50  goes  10  times 
5  in  55  goes  11  times 
5  in  60  goes  12  times 
5  in  65  goes  13  times 

3  in     6  goes     2  times 
3  in     9  goes     3  times 
3  in  12  goes     4  times 
3  in  15  goes     5  times 
3  in  18  goes     6  times 
3  in  21  goes     7  times 
3  in  24  goes     8  times 
3  in  27  goes     9  times 
3  in  30  goes  10  times 
3  in  33  goes  11  times 
3  in  36  goes  12  times 
3  in  39  goes  13  times 

S=^f^f=^f  .•&==*F^=^^>Z^^^^=37^^=&^~f^?7^-f^rF-. 

6  in  12  goes  2  times 
6  in  18  goes  3  times 
6  in  24  goes  4  times 
6  in  30  goes  5  times 
6  in  36  goes  6  times 
6  in  42  goes  7  times 
6  in  48  goes  8  times 
6  in  54  goes  9  times 
6  in  60  goes  10  times 
6  in  66  goes  11  times 
6  in  72  goes  12  times 
6  in  78  goes  13  times 

IMvision  Table.— CONTINUED. 


7 

in 

14 

goes 

2 

times 

10 

in 

20 

goes 

2 

times 

7 

in 

21 

goes 

3 

times 

10 

in 

30 

goes 

3 

times 

7 

in 

28 

goes 

4 

times 

10 

in 

40 

goes 

4 

times 

7 

in 

35 

goes 

5 

times 

10 

in 

50 

goes 

5 

times 

7 

in 

42 

goes 

6 

times 

10 

in 

60 

goes 

6 

times 

7 

in 

49 

goes 

7 

times 

10 

in 

70 

goes 

7 

.times 

7 

in 

56 

goes 

8 

times 

10 

in 

80 

goes 

8 

times 

7 

in 

63 

goes 

9 

times 

10 

in 

90 

goes 

9 

times 

7 

in 

70 

goes 

10 

times 

10 

in 

100 

goes 

10 

times 

7 

in 

77 

goes 

11 

times 

10 

in 

110 

goes 

11 

times 

7 

in 

84 

goes 

12 

times 

10 

in 

120 

goes 

12 

times 

7 

in 

91 

goes 

13 

times 

10 

in 

130 

goes 

13 

times 

8 

in 

16 

goes 

2 

times 

11 

in 

22 

goes 

2 

times 

8 

in 

24 

goes 

3 

times 

11 

in 

33 

goes 

3 

times 

8 

in 

32 

goes 

4 

times 

11 

in 

44 

goes 

4 

times 

8 

in 

40 

goes 

5 

times 

11 

in 

55 

goes 

5 

times 

8 

in 

48 

goes 

6 

times 

11 

in 

66 

goes 

6 

times 

8 

in 

5G 

goes 

7 

times 

11 

in 

77 

goes 

7 

times 

8 

in 

64 

goes 

8 

times 

11 

in 

88 

goes 

8 

times 

8 

in 

72 

goes 

9 

times 

11 

in 

99 

goes 

9 

times 

8 

in 

80 

goes 

10 

times 

11 

in 

110 

goes 

10 

times 

8 

in 

88 

goes 

11 

times 

11 

in 

121 

goes 

11 

times 

8 

in 

96 

goes 

12 

times 

11 

in 

132 

goes 

12 

times 

8 

in 

104 

goes 

13 

times 

11 

in 

143 

goes 

13 

times 

9 

in 

18 

goes 

2 

times 

12 

in 

24 

goes 

2 

times 

9 

in 

27 

goes 

3 

times 

12 

in 

36 

goes 

3 

times 

9 

in 

36 

goes 

4 

times 

12 

in 

48 

goes 

4 

times 

9 

in 

45 

goes 

5 

times 

12 

in 

60 

goes 

5 

times 

9 

in 

54 

goes 

6 

times 

12 

in 

72 

goes 

6 

times 

9 

in 

63 

goes 

7 

times 

12 

in 

84 

goes 

7 

times 

9 

in 

72 

goes 

8 

times 

12 

in 

96 

goes 

8 

times 

9 

in 

81 

goes 

9 

times 

12 

in 

108 

goes 

9 

times 

9 

in 

90 

goes 

10 

times 

12 

in 

120 

goes 

10 

times 

9 

in 

99 

goes 

11 

times 

12 

in 

132 

goes 

11 

times 

9 

in 

108 

goes 

12 

times 

12 

in 

144 

goes 

12 

times 

9 

in 

117 

goes 

13 

times 

12 

in 

156 

goes 

13 

times 

Division  in  Rhyme. 


Harriet  has  4  oranges, 
For  little  Jane  and  Mary, 

In  equal  share,  each  has  a  pair, 
The  numbers  do  not  vary. 

And  thus  we  see  Division  true  ; 

Both  have  the  4,  and  each  has  2; 

2  twos  are  then  in  four  we  know, 

And  2  in  4  Will  2  time*  go. 


Six  large  apples  Henry  had, 
To    give    to    Silas,  John,  and 
Thomas, 

And  2  he  gave  each  little  lad, 
According  to  his  promise  ; 

And  as  he  dealt  them  round, 

3  twos  in  6  were  found; 
So  2  in  6  will  3  times  go, 
Then  3  in  6  goes  twice  we  know. 

A  teacher  had  just  20  toys, 
To  give  to  4  good  little  boys, 
He  would  the  fives  in  20  teach, 
And  so  he  gave  5  toys  to  each, 

4  fives  in  20  thus  he  shows, 
And  then   5   fours,  as  each  boy 

knows ; 

So  5  into  20  will  go  4  times, 
And    4   into   20  go  5,  correctly 

chimes ; 
The  table  will  show  you  the  truth 

of  the  rhymes. 


The  Uses  of  the  Tables. 


Notation  writes  the  figures  down, 

And  Numeration  reads  them — 
Addition  makes  two  numbers  one, 

And    more   so,   when    it    needs 

them. 
Subtraction  of  two  numbers  makes 

A  third — as  you  have  seen  them — 
The  smaller  from  the  larger  takes, 

And  shows  the  odds  between  them, 
Multiplication,  in  a  word, 


Adds  much  with  little  labor, 
And  with  two  numbers  makes  n 
third,  4 

A  far  superior  neighbor. 
Division  with  two  numbers  shows 

How  many  times  attaining, 
The  less  one  in  the  larger  goes, 

And  what  there  is  remaining. 
The  large  square  table  at  a  view, 
Will  show  what  each  and  all  can  do 


17 


TABLES    OF 

MONEY,    WEIGHTS,    MEASURES,    ETC,  j 


I.  MONEY. 

Money  has  various  names,  or  rates  : 
FEDERAL,  or  that  of  the  United  States, 

Has  Eagles,  Dollars,  Dimes,  and  Cents. 
STERLING,  or  English,  which  one  sees 
In  England  and  her  colonies, 

Has  Guineas,  Pounds,  Shillings,  and  Pence. 
FRENCH,  used  in  France  through  all  her  ranks, 

Has  simple  Centimes,  Decimes,  Francs 


FEDERAL,  OR  UNITED  STATES  MONEY.-The  value  of  this    « 
money  increases  by  tens,  which  makes  it  very  simple  and  easy  to  reckon,    (i 
and  hence  accounts  are  mostly  kept  in  Dollars  and  Cents,  in  this  country.    * 


10  mills  77i.  make     - 
10  cents      - 
10  dimes 
10  dollars  - 

Observe  the  denominations 
mill,  m. 


-          1  cent,  C. 
1  dime,  d. 
1  dollar,  $. 

»  -     1  eagle,  E. 

-Eagle,  E. ;  dollar,  $  ;  dime,  d. ;  cent,  c. , 


The  mill  is  not  a  coin,  and  is  only  used  in  counting. 
Beside  money  made  of  silver,  gold,  and  copper,  there  are 
also  pieces  of  ornamented  paper  representing  money,  upon 
which  are  printed  sums  from  one  dollar  to  one  thousand ;  these 
pass  readily  for  what  is  stamped  upon  them  for  all  the  purposes 
of  business. 

We  count  10  mills  to  every  cent, 

10  cents  to  every  dime; 
10  dimes  are  in  the  dollar  spent, 
10  dollars  in  the  eagle  chime, 


1  Shilling. 


1  Sovereign. 


ENGLISH  OR  STERLING  MONEY.— This  currency  is  used  in 
England  and  the  British  colonies. 

TABLE. 

4  farthings,  qr.,  make  1  penny,  d. 
12  pence    -                                                       1  shilling,  «. 
20  shillings    -           ....         1  pound,  £,. 

5  shillings          -  -     1  crown,  c. 

20  shillings      .....         1  sovereign,  sov. 

21  shillings          -         -         -         -  1  guinea,  G. 

Observe  the  denominations — Pound,  £ ;  shilling,  s.  pence,  d. ;  farth- 
ing, qr. ;  from  the  Latin  words,  libra,  a  pound ;  solidus,  a  shilling ; 
denarius,  a  penny  ;  quadrans,  a  farthing. 

Farthings  are  marked  in  fractions  thus : — f ,  one  farthing ; 
J,  two  farthings,  or  halfpenny;  f,  three  farthings. 

The  sovereign,  which  is  made  of  gold,  is  of  the  same  value 
as  the  pound.  Whatever  costs  a  pound,  therefore,  a  sovereign 
will  pay  for.  There  is  no  coin  called  a  pound. 

4  farthings  make  one  English  penny; 
,  12  pence  are  in  one  shilling  found : 

While  21  shillings  make  one  guinea, 
And  20  shillings  form  one  pound. 

5  shillings  moke  a  silver  croicn, 
A  sovereign  is  a  golden  pound. 

SOS 
19 


FRENCH  MONEY,— Thi3  money  is  used  in  France,  and  also  in  the 
French  colonial  possessions  to  some  extent. 

TABLE. 

10  centimes,*  c.,  make  1  decime,  d. 

10  declines,! 1  franc,t/r. 

Observe  the  denominations — Franc,  fr. ;  decime,  d.:  centime,  c. 

The  five -franc  piece  is  frequently  met  with  in  this  country, 
and  passes  currently  at  94  cents.  Coins  of  a  less  number  of 
francs,  pass  also  at  the  rate  of  19  cents  to  the  franc. 

10  centimes  in  one  decime  meet, 

10  decimes  make  one  franc  complete. 

FEDERAL  and  FRENCH  are  decimal, 

They  count  by  tens  alone: 

Of  coins  it  always  take  10  small 

To  make  the  next  larger  one. 

The  ENGLISH  currency,  'tis  thought, 

To  the  same  standard  will  be  brought. 

The  guinea  then  no  more  we'll  See, 

The  pound  1000  mills  will  be  ; 

And  all  the  lower  coins  will  range, 

In  just  accordance  with  this  change. 


TROY  WEIGHT  of  silver  and  gold  disposes  • 
APOTHECARIES'  WEIGHT  is  for  doctors'  doses} 
Whatever  else  your  trade  employs, 
Comes  under  the  rule  of  AVOIRDUPOIS. 


k  Pronounced  sonteem.  f  Pronounced  d&seem. 

|  Pronounced  fraung,  or  fiank. 


TROY  WEIGHT— Is  used  to  weigh  Gold,  Silver,  Jewels,  and  Liquors. 

TABLE. 

24  grains,  gr,,  make  -         1  pennyweight,  dwt. 
20  pennyweights     -         -         -1  ounce,  oz. 

12  ounces  1  pound,  Ib. 

Observe  the  denominations—Pound,  Ib. ;  ounce,  oz. :  pennyweight, 
dKt, ;  grain,  gr. 

This  rule  for  weighing  gold,  will  state 
That  24  grains  make  one  pennyweight  : 
And  20  pennyweights  in  an  ounce  are  found, 
While  12  good  ounces  make  a  pound. 

APOTHECARIES'  WEIGHT,— -Is  used  in  mixing  doses  of  medicine, 
but  drugs  and  medicines,  like  most  other  merchandise,  are  bought  and 
sold  by  AVOIRDUPOIS  WEIGHT. 

TABLE. 
20  grains,  gr.,  make      ...         1  scruple,  0. 

3  scruples  -         -     1  drachm,  3' 
8  drachms  t                     -         -  1  ounce,      §. 

12  ounces  -  -1  pound,  }fo. 

Observe  the  denominations — Pound,  Jfo. ;  ounce,  Z. ;  drachm,  3.; 
scruple,  3. ;  grain,  gr. 

In  mixing  doses,  Doctors  say 
That  20  giains  one  scruple  weigh  ; 
3  scruples  make  one  drachm  they  hold, 
8  drachms  are  to  the  ounce  enrolled, 
And  ounces  12  for  a  pound  are  sold. 

AVOIRDUPOIS  WEIGHT— Is  used  in  weighing  all  coarse  and 
heavy  goods,  groceries,  &c. ;  and  all  metals  except  silver  and  gold. 

TABLE. 

16  drachms,  dr.,  make          -         1  ounce,  oz. 
16  ounces         •  -         -1  pound,  Ib. 

25  pounds    -  1  quarter,  qr. 

4  quarters       -  1  hundred  weight,  fwt. 
20  hundred  weight  1  tun,  T. 


Observe  the  denominations — Tun,  T.  ;  hundred  weight,  cwt. ;  quarte., 
qr. ;_  pound,  lb. ;  ounce,  »z. ;  drachm,  dr. 

2000  pounds  make  a  tun  in  the  table ;  when,  as  it  some- 
times is,  it  is  2240  Ibs.,  28  pounds  make  a  quarter.  Except  in 
special  cases,  the  tun  is  now  regarded  as  2000  pound*  by 
the  principal  merchants  of  our  cities. 

16  drachms  make  one  ounee, 

16  ounces  make  one  pound, 
25  pounds  one  quarter  counts, 

4  quarters  make  a  hundred  round ; 
And  20  hundred  weight  are  run, 
To  make  a  full  and  perfect  tun. 

'Twas  once  absurdly  held  and  said 
112  pounds  make  a  hundred  weight; 

And  then  this  table  always  read, 
That  a  quarter  hundred  was  28 


BY  different  measures,  we  obtain 
Due  quantities  of  wood  or  grain, 
Of  cloth,  or  land,  or  wine,  and  tell 
How  much  of  each  we  buy  or  sell. 
CLOTH  MEASURE  is  for  ribbons,  tapes, 
And  cloths,  and  silk,  for  coats  or  capes. 
LONG  MEASURE  serves  to  tell  and  trace 
The  distances  from  place  to  place. 
SURVEYORS'  MEASURES,  understand, 
Are  only  used  in  measuring  land. 
DRY  MEASURE  tells  how  much  we  gain 
Of  salt,  coal,  fruit,  potatoes,  grain  ; 
While  LIQUID  MEASURE  justly  classes 
Wine,  spirits,  beer,  oil,  milk,  molasses. 
SQUARE  MEASURE  deals  with  surfaces, 
As  walls,  and  floors,  and  fields,  and  seas; 
And  CUBIC  MEASURE  ascertains 
What  any  solid  shape  contains. 
TIME  MEASURE  tells  us,  as  they  fly, 
How  days,  months,  years,  are  ruSm'ng  by; 
And  CIRCULAR  MEASURE  shows  the  worth 
Of  lines  that  circle  round  the  earth, 
And  of  the  bands  which  reason's  eye 
Traces  across  the  glittering  sky. 


1.     MEASURES     OP     LENGTH. 

CLOTH  MEASTJ&E— Is  used  to  measure  Cloths,  Ribbons,  Tapes, &c. 

TABLE. 

2f  inches,  in.,  make  1  nail,  n. 

4    nails  ...     1  quarter  of  a  yard,  qr. 

4  quarters  1  yard,  yd. 

FOREIGN  CLOTH    MEASURES. 

2|  quarters,  make   -         -         1  ell  Hamburgh,  E.  H. 
3    quarters          -  -     1  ell  Flemish,  E.  F. 

5  quarters      -         -         -         1  ell  English,  E.  E. 

6  quarters  -         -         -     1  ell  French,  E.  Fr. 
Observe  the  regular  denominations — Yard,  yd. ;  quarter,  qr. ;  nail,  n.  f 

inch,  in. 

In  measuring  cloth  for  use  or  sale, 

2  J  inches  make  one  nail ; 

4  nails  one  quarter  we  regard, 

And  four  full  quarters  make  one  yard.  • 

Nails  now  are  seldom  used,  we've  heard, 

Eighths  and  sixteenths  are  much  preferred. 

LONG  MEASURE— Is  used  to  measure  distances,  and  to  ascertain 
the  length  of  anything  without  regard  to  breadth. 

TABLK. 

10    lines,  /.,  make       ...  1  inch,  in. 

12    inches 1  foot,  ft. 

3    feet      .....  1  yard,  yd. 

5^  yards        -         -         -         -  1  rod  or  pole,  p. 

40    poles,  or  220  yards  1  furlong,  fur. 

8    furlongs 1  mile,  M. 

3    miles 1  league,  L. 

geographic,  or  69 \  statute  miles  1  degree,  Deg. 


Twelve  lines  make  an  inch  in  France. 

In  measuring  the  height  of  horses  the  hand,  4  inches,  is 
used  ;  and  in  measuring  the  depth  of  water,  the  fathom,  6  feet, 
w  uoed. 

In  measuring  distances  or  lengths, 
10  linen  are  said  to  make  one  inch; 
12  inches  make  a  perfect  foot, 
3  feet  into  a  yard  are  put ; 
5  2  yards  make  a  rod  or  pole, 
And  40  rods  a  furlong  whole  ; 
8  furlongs  make  a  mile  quite  big, 
And  3  full  miles  make  up  a  league. 
In  measuring  round  the  earth,  we  gee, 
That  60  miles  make  one  degree; 
Degrees  360,  then, 
The  earth's  circumference  will  span. 


SURVEYOR'S  MEASURE.— This  measure  is  used  in  ascertaining 
the  length  and  breadth  of  land,  roads,  &c. 

TABLE. 

7  92-100  inches,  in.,  make  1  link,  J. 
25  links  ------     1  pole,  p. 

4  poles,  or  100  links  -  1  chain,  c. 

10  chains          -         -         -         -   '      -     1  furlong,  fur 

8  furlongs  ...         1  mile,  M. 

Observe  the  denominations — Link,  1. ;  pole,  p. ;    chain,  c. ;   furlong, 
fur. ;  mile,  M. 

7  inches  and  ninety-two  hundredths,  make 
One  link  in  the  chain  surveyors  take, 
100  links  his  chain  embraces, 
With  80  chains  one  mile  he  traces. 


2.    MEASURES    OF    CAPACITY. 

LIQUID  MEASURE— Is  used  in  measuring  Wine,  Spirits,  Beer,  Oil, 
Vinegar,  Milk,  Molasses,  &c. 

TABLE. 

4    gills,  g.,  make  1  pint,  pi. 

2    pints     -         -         -         •         -     1  quart,  qt. 
4    quarts  *         •         -         1  gallon,  gal. 

31§  gallons  -         -  1  barrel,  bbl. 

2    barrels       ....         1  hogshead,  hhd. 
2    hogsheads     ....     1  pipe,  p. 
2    pipes  ....          1  tun,  t. 

Observe  the  regular  denominations — Tun,  t. ;  pipe,  p. ;  hogshead,  khd.  ; 
barrel,  bbl. ;  gallon,  gal. ;  quart,  qt. ;  pint,  pt. ;  gill,  g. 


24: 


TABLE. 

9  gallons,  g.,  make    - 

10  gallons       - 

2  firkins,  or  18  gallons 

2  kilderkins,  or  36  gallons 
1 J  barrels,  or  54  gallons 

42  gallons       - 

2  tierces,  or  84  gallons 


1  anker,  a.  • 

1  kilderkin,  Jc. 

1  barrel  of  beer,  &c.  bbl. 

1  hogshead  of  beer,  khd. 

1  tierce,  t. 

1  puncheon,  p. 


Most  liquids  are  now  sold  by  the  gallon,  quart,  and  pint,  and 
not  by  the  other  denominations  of  liquid  measure  ;  in  fact, 
vessels  are  rarely  made  to  hold  the  exact  quantities  stated  in 
the  table,  and  frequently  retain  the  names  though  containing 
much  more,  the  hogshead  and  barrel  for  instance. 

In  measuring  liquids,  first  we  take 

4  little  gills  one  pint  to  naoke  ; 

2  pints  then  make  one  quart,  and  still 

4  quarts  the  gallon  measure  fill. 

Gallons  one  half  and  31, 

Will  fill  a  barrel  to  the  bung. 

2  barrels  to  the  hogshead  go, 

2  hogsheads  fill  a  pipe,  and  so 

2  pipes  will  near  a  tun  o'erfiow. 


Though  many  good  things  are  measured  still 
By  gallon,  quart,  and  pint,  and  gill, 
Yet  Liquid  Measure  oft  seems  to  me 
"  The  measure  of  human  misery." 
For  O,  what  countless  evils  come 
From  brandy,  whiskey,  gin,  and  rum, 
Which  it  were  better  ne'er  to  touch, 
For  a  single  drop  is  "  a  drop  too  much." 


DRY  MEASURE— Is  used  in  measuring  Grain,  Potatoes,  Fruit,  Coal, 

Salt,  Seeds,  &c. 


2  pints,  pt.,  make 
8  quarts  - 

4  pecks 

36  bushels          ... 
8  bushels      - 

Observe  the  regular  denominations 
peck,  p. ;  quart,  qt. ;  pint,  pt. 


1  quart,  qt. 
1  peck,/?. 
1  bushel,  bush. 
1  chaldron  of  coal,  chal. 
1  quarter  of  corn,  qr. 
— Chaldron,  chal. ;  bushel,  busk.  ; 


2  pints  DRY  MEASURE  make  one  quart, 
8  quarts  one  honest  peck  contains, 

4  pecks  are  in  a  bushel  brought ; 

8  bushels,  if  you  are  measuring  grains, 

Are' to  the  quarter*  counted  out; 

But  if  bituminous  coal,t  you  take 

s^Then  6  and  30  bushels  make 

The  chaldron,  which  in  trade  obtains, 

3.    MEASURES    OF    CONTENT. 

LAND  OR  SQUARE  MEASURE— Is  used  in  reckoning  tht  con- 
tents  of  any  surface  by  its  length  and  breadth. 

TABLE. 

144    square  inches,  s.  era.,  make  1  square  foot,  S.  F. 
9     square  feet    -         -         -     1  square  yard,  S.  Y. 
30  j  square  yards 


4 
J 


40    square  poles - 
4    square  roods 
640    square  acres  - 
Observe  the 


I  square  rod,  pole,  or   . 

perch,  S.  P. 
1  square  rood,  S.  R. 
1  square  acre,  S.  A. 
1  square  mile,  S.  M. 


[nations — Square  mile,  S.  M. ;  square  acres,  S.  A. , 
square  rood,  S.  R. ;  square  perch,  S.  P. ;  square  yard,  S.  Y. ;  square  foot, 
5.  JP. ;  square  inch,  S.  I. 

Square  inches  one  hundred  and  forty-four 

Make  one  square  foot,  and  nothing  more. 

9  square  feet  make  one  square  yard, 

30  yards  and  a  quarter  are  one  pole  squared; 

40  square  poles  make  one  square  rood, 

Yet  4  square  roods  make  an  acre  good ; 

And  acres  640  the  while, 

Are  wanted  to  make  up  one  square  mile. 


SOLID  OR  CUBIC  MEASURE— Is  used  to  reckon  the  contents  of 
anything  by  its  length,  breadth,  and  depth. 

TABLE. 

1728  solid  inches,  s.  in.,  make 
40  feet  of  round,  or 
50  feet  of  hewn 
27  solid  feet 
16  solid  feet  of  wood 
8  cord  feet  of  wood    - 


timber 


1  solid  foot,  S.  F. 
1  tun,  Tun. 


1  solid  yard,  S.  Yd. 

1  cord  foot  of  wood,  Ft.  IV. 

1  cord,  C. 


Observe  the  denominations — Cord,  C. ;  cord  foot  of  wood,  Ft.  W. , 
solid  yard,  S.  Y. ;  solid  foot,  S.  F. ;  solid  inch,  S.  I. 


*  Wheat  is  measured  in  Great  Britain  bv  the  quarter  of  480  Ibs. 
t  Bituminous,  or  soft  coal,  is  sold  by  measure,  and  anthracite,  or  hard 
coal,  by  weight. 


One  thousand  seven  hundred  and  twenty-eight 

Inches  one  solid  foot  complete. 

In  timber,  40  feet,  if  round, 

Or  50  hetcn,  a  tun  is  found. 

In  measuring'  ships  the  rule  must  run, 

Feet  2  and  40  make  a  tun. 

Feet  27  one  solid  yard  we  rate, 

A  cord  of  wood  one  hundred  twenty-eight. 


4.    MEASURES    OF    DURATION    AND    CIRCULAR    DISTANCES. 

TIME  MEASURE— Is  used  in  computing  the  different  periods  in 
which  any  transaction  or  event  occurs. 

TABLE.     , 

60  seconds,  sec.,  make  1  minute,  m. 

60  minutes  •         -     1  hour,  k. 

24  hours        -  1  day,  d. 

7  days     -  ...     1  week,  w. 

4  weeks      -  ...         1  month,  mo. 

12  months          -         -         -         -         -     1  year,  yr. 
100  years  ....         1  century,  C. 

Observe  the  denominations  —  Century,  O.  ;   year,  yr.  ;   month,  mo.  • 
week,  w.  f  day,  d. ;  hour,  \. ;  minute,  m. ;  second,  sec. 

12  calendar  months,  or  13  lunar  months,  1  day,  ard  6  hours, 
or  365  days,  6  hours,  1  common,  or  Julian  year. 
The  year  is  divided  by  the  calendar  as  follows : — 

DATI. 


1 


1st  month,  January,  has     31 


2d 
3d 
4th 
5th 
6tr 


February, 

March, 

April, 

May, 

June, 


28 
31 
30 
31 
30 

181 


7th  month,  July,  has 
8th       "        August, 
9th       "        September, 
10th       "        October, 
llth       "        November, 
12th        "        December, 


BATS. 

31 
31 
30 
31 
30 
31 

3~65    f3 


February  has  29  days  every  fourth  year,  which  is  called  Bis- 
sextile, or  Leap  Year.  Every  Leap  Year  may  be  divided  by  4 
without  a  remainder;  other  years,  divided  by  4,  leave  one, 
which  shows  their  number  after  Leap  Year.  Thus,  1854 
divided  by  4,  leaves  a  remainder  of  2  :  that  is,  'It  is  the  second 
after  Leap  Year,  &c.,  &c. 

The  number  of  days  in  each  month,  may  easily  be  remem- 
bered by  the  following  verse  : — 

Thirty  days  have  September, 
April,  June,  and  November ; 
All  the  rest  have  thirty-one, 
Excepting-  February  alone, 
Which  hath  twenty-eight,  nay  more, 
Hath  twenty-nine  one  year  in  four. 

There  are  in  every  year  four  seasons,  viz:  SPRING,  SUMMER, 
AUTUMN,  and  WINTER. 

The  Spiing  months  are  March,  April,  and  May. 
The  Summer  months  are  June,  July,  and  August. 
The  Autumn  months  are  September,  October,  and  November. 
The  Winter  months  are  December,  January,  and  February. 
The  Spring  is  the  season  of  flowers;  the  Summer  of  fruits  ; 
the  Autumn  of  the  decay  of  vegetation  and  the  fall  of  the  leaf; 
and  the  Winter  of  frost  and  snow. 

60  seconds  make  1  minute, 

Time  enough  some  good  to  do ; 
60  minutes  make  1  hour, 

Who  will  dare  to  waste  it  1     Who  ? 
24  hours  make  up  the  day, 
It  Time  for  work,  and  sleep,  and  play ; 

7  days  to  the  week  are  given, 
Six  for  toil  and  one  for  heaven. 
God  gives  me  six  for  work  and  play 
I  will  not  steal  .the  seventh  away. 
4  weeks  in  every  month  appear, 
12  months  make  up  the  rolling  yeat , 
100  years — few  live  them  to  see — 
Are  what  are  called  a  century. 


CIRCULAR  MEASTJRE— Is  used  by  Astronomers,  Navigators,  &c, 
in  making  their  calculations. 

TABLE. 

60  seconds,  "  make     - 
60  minutes      - 
30  degrees  ... 

12  signs,  or  360  degrees 

Observe  the  denomination! 
second, ". 


1  minute,  ' 

1  degree,  ° 

1  sign,  S. 

1  circle  of  the  Zodiac,  C. 


Circle,  C. ;  sign,  S. ;  degree,  °  ;  minute,' 


60  seconds  make  one  minute, 

CO  minutes  one  degree: 
30  degrees  one  sign  has  in  it, 
circle 


'Tis  knowledge  gained  from  this,  that  guides 
The  ship,  that  o'er  the  ocean  rides, 
And  shows  the  pilot  hjow  to  steer 
From  place  to  place,  remote  or  near. 


IV,  BOOKS,  PAPER,  AND  PARCHMENT. 

BOOKS,  PAPER,  PARCHMENT,  all  concern 
Men  of  a  literary  turn: 
As  authors,  printers,  and  booksellers— 
A  race  of  genuine  clever  fellows — 
The  paper  manufacturer,  too, 
With  these,  of  course,  has  much  to  do ; 
The  stationer  and  binder  then — 
Known  as  industrious,  thrifty  men- 
Bear  each  an  honorable  part 
In  the  noble,  intellectual  art, 
Of  furnishing  the  mind  and  heart. 


1.    PAPER    AND     PARCHMENT, 

TABLE  OF  PAPER  AND  PARCHMENT. -This  table  la  used  by 
Papermakers,  Printers,  and  dealers  in  Stationery,  &c.,  &c. 

TABLE. 

24  sheets  of  paper,  make  1  quire,  qr. 

20  quires  1  ream,  Rm. 

2  reams         - 


10 


reams    - 


-     1  bale,  Bl. 


3n  sheets  one  quire  will  take, 
'     And  20  quires  one  ream  composes  J 
2  reams  we  in  a  bundle  make, 
10  bundles  a  full  bale  enclose*. 


By  dozens  parchment-skins  are  told ; 
12  to  the  dozen,  as  of  old ; 
5  dozen  for  a  roll  are  sold. 

The  different  sizes  of  paper  are — Foolscap,  post,  demi, 
medium,  royal,  super-royal,  imperial,  and  elephant.  Larger 
papers  ars  described  by  their  length  and  breadth  in  inches  j 
thus,  20  by  32,  24  by  38,  26  by  40,  29  by  44,  &c.,  &c. 


2.    SIZES    OF   BOOKS. 

TABLE  OF  BOOKS.— This  table  is  used  by  Authors,  Printers,  and 
Booksellers,  in  ascertaining  and  naming  the  sizes  of  books.     . 

TABLE. 

1  sheet  of  paper  folded  into    2  leaves  is  a  folio,  Fol. 
1  sheet  of  paper  folded  into    4  leaves  is  a  quarto,  4to. 
1  sheet  of  paper  folded  into    8  leaves  is  an  octavo,  Svo. 
1  sheet  of  paper  folded  into  12  leaves  is  a  duodecimo,  12w?0. 
S     1  sheet  of  paper  folded  into  18  leaves  is  an  octodecimo,  ISmo. 

Observe  the  denominations — Folio,  fol. ;  quarto,  4to. ;  octavo,  Svo. ; 
duodecimo,  12mo. ;  octodecimo,  18mo. 

Whoever  with  a  book  engages, 
Well  knows  each  leaf  will  count  2  pages ; 
One  folio  sheet  2  leaves  will  rate, 
A  quarto  4,  octavo  8 ; 
A  duodecimo*  a  dozen  clean, 
An  octodecimo  eighteen ; 
Vicessimo  quarto  makes  up  twenty-four. 
Tricessimo  secundo  thirty-two,  no  more. 


*  The  duodecimo,  octodecimo,  vicessimo  quarto,  and  tricessimo 
eecundo,  which  are  Latin  numerals,  are  generally  called  12mo.,  18mo., 
24mo.,  and  32mo.  There  are  also  48mo.,  64mo.,  and  72mo. 


1,  TABLE  OF  WEIGHTS, 

A  barrel  of  flour  weighs  196  Ibs. 

A  barrel  of  beef  or  pork             •  200    " 

A  barrel  of  pot  ashes     •  200    " 

A  firkin  of  butter 56    " 

A  bushel  of  salt 56    " 

A  peck  of  salt 14    " 

A  gallon  of  train  oil                 -         -         -  7\  " 

A  stone  of  wire  weighs      •  10^  " 

A  stone  of  sheet  iron,  or  horseman's  weight  14    " 

A  quintal  of  fish 100    " 

A  faggot  of  steel 120    " 


A  fother  of  lead 


2184 


2.  TABLE  OF  PARTICULARS. 

12  things  make  1  dozen,  doz. 

12  dozen,  or  144          -         -         -  1  gross,  gro. 

12  gross  or  1728  1  great  gross,  g.  gro. 

20  things 1  score. 

5  score  ....  1  hundred,  C. 


3,  VALUE  OF  SILVER  AND  GOLD  COINS, 


as. 
24 
20 
84 
84 


An  English  shilling         ..... 

"          "       crown 1 

"         "       sovereign     .....     4 

"       pound      4 

"         "       guinea          -         -         -         -         -     5  00 
A  franc  of  France      -  19 

A  thaler  of  Germany      -          ....         67 
A  Spanish  doubloon   -         -         -         -  16  00 

A  South  American  doubloon  -         -         -         -  15  60 
Four  shillings  and  two  pence  sterling         -  1  00 

4,  OLD  ENGLISH  COINSL 


A  groat  • 
A  tester 
A  noble  • 
An  angel 
A  mark 


5.  TABLES  OF  ALIQUOT,  OK  EVEN  PARTS. 
Being  fractions  or  broken  parts  of  certain  things  and  their  value 

Parts  of  a  Dollar.      Parts  of  a  Shilling.       Parts  of  a  Pound. 


penny    is 
pence  are 


Parts  of  a  Penny. 

1  farthing  is 

2  far tli's  are 


Parts  of  a  Cwt.  (Parts  of  a  Tun 


Parts  of  a  Year 
of  12  months. 

1  mo.   is 

2  mos.  are 

3  "      " 


Parts  of  a  Cwt 
of  100  Ibs. 


of22401bs. 

cwt.  grs. 

1  0   is 

2  0  are 


Fractions  in  Arithmetic  are  so  made,  that  if  all  the  parts 
into  which  a  number  is  divided  are  added  together,  they  will  just 
equal  that  number;  as  when  an  apple  is  cut  into  parts  of  various 
shapes,  you  can  join  them  together  and  form  the  apple  again. 


6,  TABLES  OF  STERLING  CURRENCY, 


Table  of  Shillings  and  Pence, 


1  is 

2  are 

3  " 

4  " 

5  " 

6  " 

7  " 

8  " 

9  " 

10  " 

11  " 
12"  " 


d. 

12 

24 

36 

48 

60 

72 

84 

96 

108 

120 

132 

144 


d.  s.    d. 

20  are    1     8 

30    "      26 

40 

50 

60 

70 

80 

90 
100 
110 
120 
130 


3  4 

4  2 

5  0 

5  10 

6  8 

7  6 

8  4 

9  2 
10     0 
10  10 


Table  of  Shillings  and  Pounds.     L 


20  are 

30  " 

40  " 

50  " 

60  " 

70  " 

80  " 

90  " 

100  " 

110  " 

120    " 

130  " 


jg    s. 
1     0 

1  10 

2  0 

2  10 

3  0 
10 

0 
10 

0 
10 


6     0 

6  10 


£  s. 
140  are  7  0 
150 
160 
170 
180 
190 
200 
210 
220 
230 
240 
500 


7  10 

8  0 

8  10 

9  0 
9  10 

10  0 

10  10 

11  0 

11  10 

12  0 
25  0 


In  Maine, 
1   New  Hampshire, 
"    Vermont, 
"    Massachusetts, 
"    Rhode  Island, 
"    Connecticut 
"    Virginia, 
"    Kentucky, 
"   Tennessee, 

In  New  York, 

"    Ohio, 

"    North  Carolina, 


In  New  Jersey, 
"    Pennsylvania, 
"    Delaware, 
"    Maryland, 


16f  cents  are  called 

one  shilling1, 

and  six  shillings 

make  one 

dollar. 


12 1  cents  are  called 

one  shilling, 
and  eight  shillings 
make  one  dollar./ 

13 1  cents  are  called 

one  shilling, 

and  seven  shillings 

and  sixpence  make 

one  dollar. 

21  2-5  cents  are  called 

one  shilling, 
and  four  shillings 
and  eight  pence 
make  one  dollar. 


7.    TABLE    SHOWING    THE    SHILLINGS   AND    PENCE 

Currency  of  the  principal  States  of  the  Union  and  the  British  Provinces, 
with  its  Value  in  Dollars  and  Cents. 


In  the  remaining  thirteen  States,  the  cent,  dime,  and  dollar, 
of  Federal  money,  are  generally  used. 


BRITISH 

In  Canada  East, 
"    Canada  West, 
"    Nova  Scotia, 
"    New  Brunswick 


PROVINCES. 

^|  20  cents  are  called 

!  one  shilling, 

and  five  shillings 
make  one  dollar. 


10.  TABLE  0?  ARITHMETICAL  SIGNS. 

+  Pcus,  or  more,  meaning  added  to.  This  sign  when  placed 
between  two  numbers,  shows  that  they  are  to  be  added  to- 
gether and  considered  as  one  number;  thus,  24+36  ;  that  is,  24 
added  to  36,  which  is  read  24  plus  36. 

=  dEqualitas,  or  equality,  meaning  equal  to.  This  sign  when 
placed  between  two  or  more  numbers,  shows  that  those  which 
precede  the  sign  are  equal  to  those  which  follow  it;  thus, 
24+36=60 ;  that  is,  24  added  to  36  are  equal  to  60. 

—  Minus,  or  less,  meaning  subtracted  from.  This  sign, 
when  placed  between  two  numbers,  shows  that  "one  is  to  be 
taken  from  the  other ;  thus,  84  —  42  ;  that  is,  42  is  to  be  sub- 
tracted from  84,  which  is  read  84  minus  42. 

X  Multiplied,  to  multiply,  meaning  multiplied  by.  This 
sign  placed  between  two  numbers  signifies  that  one  is  to  be 
multiplied  by  the  other;  thus,  24X36  ;  that  is,  24  is  to  be  mul- 
tiplied by  36,  which  is  read  24  multiplied  by  36. 

-t-  Divido,  to  part,  meaning  divided  by.  This  sign  placed 
between  two  numbers  shows  that  one  is  to  be  divided  by  the 
other ;  thus,  60-?- 15  ;  that  is,  60  is  to  be  divided  by  15.  When 
placed  horizontally  between  two  numbers,  the  one  above  and 
the  other  below,  the  dots  are  dispensed  with ;  thus,  J ;  that 
is,  1  divided  by  2. 

EXAMPLES. 

Read  the  following :  72+47=119;  656+809=1465;  1400 
+700=2100  ;  76  —  38=38  ;  104—26=78 ;  290  —  145=145  ; 
25X12=300;  99X9=891;  425X50=21250;  64-f-8=8; 
144-^12=12;  1728-v-12=144;  1728+144  — 576X12-7-288 
=54;  64-1-8X16=128;  36X12=144X3;  500X10  —  300= 
47X90+470;  4  —  2X6=12. 

Vinculum,  or  a  bond  of  union,  meaning  that  the  num- 
bers over  which  it  is  placed,  are  to  be  considered  as  united 
or  one,  and  to  be  subjected  to  the  same  operation ;  thus, 
12+13X19. 


1  ::  :  Proportio,  or  proportion.  These  signs  are  placed  be- 
tween numbers  to  show  their  relation  to  each  other,  so  that 
knowing  the  relation  of  two  numbers,  two  others  may  be  found 
that  have  the  same  relation;  thus,  3  :  6  ::  9  :  18,  which  is 
read  as  follows  I  As  3  is  to  6  so  is  9  to  18,  because  3  is  the 
half  of  6  and  9  half  of  18,  therefore  the  proportion  of  3  to  6 
is  the  same  as  9  to  18.  This  sign  is  read  thus:  As,  is  to, 
«o  is,  to. 

,  ">  s  Polentia,  or  power.  Evory  number  is  a  power,  and  to  in- 
crease its  power  you  must  multiply  it  by  itself  the  number  of 
times  answering  to  the  power  to  which  you  wish  to  raise  it. 
The  figure  which  expresses  the  power  to  which  another  is  to 
be  raised  is  called  an  exponent  or  index,  which  is  a  small 
figure  placed  against  its  right  hand  upper  part;  thus,  43;  that 
is,  4  is  to  be  multiplied  three  times  by  itself,  or  4X4X4=64; 
therefore,  64  is  the  third  power  of  4,  ana  is  the  same  as  43. 

\S  Radix,  or  root,  meaning  that  the  root  is  to  be  extracted. 
The  root  of  a  number  is  such  a  one  as  multiplied  by  itself  a  given 
number  of  times  will  produce  the  number  whose  root  is  wanted. 
V  means  the  square  root,  3V  the  cube  root,  4V  the  fourth 
root,  BV  the  fifth  root,  &c. ;  therefore,  V64  shows  that  8  is 
wanted,  because  8X8=64.  3V64  shows  that  4  is  wanted,  be- 
cause 4X4X4=64.  4V16  shows  that  2  is  wanted,  because 
2X2X2X2=16.  5v/243  shows  tnat  3  is  wanted,  because 
3X3X3X3X3=243. 

ILLUSTRATIVE  EXAMPLES, 

ODD    NUMBERS. 

Odd  numbers  begin  with  1,  and  consist  of  every  second  fol- 
lowing figure;  thus,  1,  3,  5,  7,  9,  11,  13,  15,  17,  19,  are  odd 
numbers. 

Odd  numbers  X  by  odd  numbers  =  odd  numbers. 

Odd  numbers  X  even  numbers  =*  even  numbers. 

Even  numbers  X  even  numbers  =  even  numbers. 

Even  numbers  -{-  even  numbers  =  even  numbers. 

Odd  numbers  -j-  odd  numbers  =*  even  numbers. 

Odd  numbers  -j-  even  numbers  =  odd  numbers. 

Many  of  the  odd  numbers  above  3  that  can  only  be  ~f-  1,  can 
be  -T-  6  by  subtracting  ]  or  adding  1.  For  instance,  13  can 
only  be  -j-  1  but  13  —  1  may  be  -f-  6,  so  with  17,  19,  25,  &c. 

WHAT  is  A  TRILLION  ?  a  thousand  billions  ;  written  thus— i 
1,OOO,OOO,OOO,OOO. 

But  if  you  were  to  count  200  a  minute,  it  would  take  you  95J2 
years  34  days  5  hours  and  20  minutes  to  count  it,  which  la 
nearly  twice  as  long  as  the  world  has  existed 


THE    NUMBER    NINE. 


The 


of  the  figure  9  ; 


and 


ark- 


ore  numerous 
able  than  those  ot  any  other  figure. 

The  figures  composing  the  product  of  every  figure  from  1  to  9 
multiplied  into  9,  added  together,  make  NINE  ;  thus— 
99  9 

1  4 7 


9.  9         36.  3+6=9         63.  6+3=9 
258. 

18.  1+8=9 
3 

45.  4+5=9 
6 

72.  7+2=9 
9 

27.  2+7=9         54.  5+4=9         81.  8+1 

The  above  multipliers  from  1  to  9  added  together=45  and 
4+5=NiNE.  Their  several  products  added  together  =405, 
which  -+  9=45  and  4+5=NiNE.  The  amount  of  the  first 
product  (9)  ao»led  to  the  remaining  eight  products  (eight 
9s)=81,  and  8+l,=9  and  81=9X9;  81  is  therefore  called 
the  square  of  NINE.  The  405  mentioned  above  +  81=486, 
and  this  -5-9=54,  and  5+4=NiNE.  The  number  of  changes 
that  may  be  rung  on  9  bells  is  362,880,  which  figures  added 
together  make  27,  and  7+2=NiNE.  And  362,880-j-9=40,320, 
and  these  figures  added  together  make  NINE. 

THE    GAME    OF    CHESS. 

Sessa,  who  invented  the  game  of  chess  for  an  East  Indian 
king,  was  promised  in  return  any  reward  which  he  should  ask. 
Understanding,  better  than  his  patron,  the  power  of  numbers, 
and  wishing  to  rabuki  his  rashness,  he  asked  simply  for  one 
grain  of  wheat  for  the  first  square  on  the  chess-board,  two  for 
the  second,  four  for  the  third,  and  so  doubling  to  the  sixty- 
fourth.  The  %king  was  astonished  at  the  apparent  smallness 
of  the  gift,  but  still  more  so,  when  told  that  the  number  of 
grains  would  be  18,416,744,073,709,551,615,  There  are  in  a 
bushel  589,824  grains  of  wheat,  and  18,446,744,073,709,551,615 
-j-589,824  gives  31,274,997,411,295  bushels;  more  than  the 
whole  surface  of  the  earth  could  produce  in  many  years,  and 
more  in  value  probably  than  the  whole  wealth  of  the  globe. 
The  king,  therefore,  did  not  keep  his  promise  .' 

GEORGE    BIDDER. 

This  wonderful  boy,  whose  portrait  is  on  the  title-page, 
when  very  young  and  uneducated,  could  solve  the  most  difficult 
arithmetical  questions  entirely  in  his  own  mind  without  the  use 
of  pencil  or  slate,  and  more  quickly  than  any  one  could  in  the 
common  way. 


(«^utm{*^*tt:s^tt^<ttittf<mtt^&®[*mi.\ 


36 


9      ^ 


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